We prove two theorems concerning Lyapunov functions on metric spaces. The new element in these theorems is the lack of a hypothesis of compactness or local compactness. The first theorem applies to a ...

Topological groups, which integrate algebraic group structures with continuous topologies, and metric spaces, defined by a distance function, form a fundamental basis for modern mathematical analysis.

We give a systematic technical exposition of the foundations of the theory of computably compact metric spaces. We discover several new characterizations of computable compactness and apply these ...